Pre-lecture resources

These resources are pulled together from various online sources. I've tried to be as specific as possible to the problems in the pre-lecture assignments. However, many related videos can be found by the same authors as those posted below. If you find other videos (or other resources) that you found particularly useful, let me know.

Please send me requests for more suitable supplements when these do not prove sufficient.

Pre-lecture assignment	link
Week 1 - Thurs	Plugging in to check a solution
	Tuesday's lecture slides
	Integrating factors by commutant (both the linked video and it's follow-up are useful)
	Separating variables by commutant
Week 2 - Tues	Second order linear homogenous equation with constant coefficients by Kahn Academy.
	Salt water flowing in and out of a tank by commutant
Week 2 - Thurs	Section 2.3.1 of Notes on Diffy Qs
	Wronskian and linear independence
	A review of complex numbers
Week 3 - Tues	Complex roots of the characteristic equations by PatrickJMT.
	Repeated Roots by Chris Tisdell or this one by SolveandGo on the same topic.
Week 3 - Thurs	Method of undetermined coefficients by Houston Math Prep. First 4 minutes (general idea) and examples at 12:15 and 23:00.
	Method of undetermined coefficients by Chris Tisdell. Start watching at 15:05 for help with Problem 1 part c.
Week 4 - Tues	Linear Combination of Sine and Cosine functions by SLCC Math Department. This video shows you how to convert from a sum of trig functions to a single cosine function. In the pre-lecture problems, you're asked to convert to a single sine function so you'll have to figure out how to modify the approach in the video appropriately - you just have to use a different trig identity but the rest is similar.
	Introduction to Vibrating Systems by Chris Tisdell. 1:07-4:45 for basic model. Forced vibrations starts at 15:50.
Week 4 - Thurs	Writing an equation from a sin/cos graph
	Damped oscillations
Week 5 - Tues	Converting a 2nd order ODE into a system of 1st order ODEs
	Calculating the determinant
	From system of eqs to matrix
Week 5 - Thurs	Eigenvalues and eigenvectors by PatrickJMT. The example starts at 1:20.
Week 6 - Tues	Refer to linear algebra resources (MATH 152 text or similar)
Week 6 - Thurs	No pre-lecture assignment.
Week 7 - Tues	System of ODEs with a repeated eigenvalue by Eric Cytrynbaum
Week 7 - Thurs	No video. Note that a steady state solution must have zero derivative.
Week 8 - Tues	Laplace transform playlist (including: Intro to Laplace transform, Transform of a sum of functions (linearity), and Transform of cos(2t))
	Finding the inverse transform of 2/(s-3).
	Partial fraction decomposition by PatrickJMT
Week 8 - Thurs	Short version of PJMT below skipping details of things covered previously.
	Introduction to the Heaviside function and steps for writing a piecewise function in terms of Heavisides.
	Laplace transform of the Heaviside function by Eric C
	Solving non-homogeneous equations using Laplace transforms by PatrickJMT
	A table of transforms by Paul Dawkins
Week 9 - Tues	Intro to delta functions by Kahn. This video is long but the first few minutes should serve as a good intro.
	Integrals with delta functions by MathPhysicsQuestions
Week 9 - Thurs	Convolution by MathDoctorBob
Week 10 - Tues	REPLACE: Fourier series made easy by Randell Heyman. - make one specific to ww question.
	Square wave example
	Fourier series introduction by commutant.